Many appliances exist for cutting bands; examples are described in U.S. Pat. Nos. 2,889,975 to HANLON and 3,138,985 to MILLS. However, in HANLON, a blade is punched through the band, which would be inoperative with surgical packs, whereas in MILLS, moving rolls press the band onto a blade, which has the effect of blunting the edge of the blade. The harder the pack is to cut, the faster the blade becomes dull.